I would recommend you take a look at a similar app called Authy https://authy.com/. I have a similar issue of using 2 different mobile devices and needing to have access to my authenticator on either device. Authy uses a google auth compliant totp implementation which allows you to scan the same qrcodes that google and others provide to import the token into the app on one device. Once you have the token imported on that device you tell authy to backup your tokens and on the second device you do a restore. Once done your token will be available on either device.

yes if you are already using google authenticator or other similar apps you will need to turn it off and re-setup 2fa using authy as its usually not possible to access the original seeds used. Once you get everything setup in authy on a device it will restore and sync to the second device trivially and adding new authenticators on either device will sync to the others but prompt you for your backup password. I just enrolled the authy desktop app this morning and had everything ready to go in seconds.